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A new natural structural congruence in the pi-calculus with replication

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Abstract.

In the \(\pi\)-calculus with replication, a new structural congruence called “middle” congruence is investigated: a notion of structural equivalence of processes in which replication of a process is viewed as a potential rather than an actual infinite number of copies of the process, in the sense that copies are spawned at need rather than produced all at once. It is slightly weaker than standard congruence (which is also of the potential type) but stronger than the extended congruence investigated before by the authors (which is of the actual type). It is shown that middle congruence has the same desirable properties as extended congruence: it is decidable and it has a concrete multiset semantics. Thus, these properties do not depend on the distinction between potential and actual replication.

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References

  1. Berry, G., Boudol, G. (1992) The chemical abstract machine. Theoret. Comput. Sci. 96: 217-248

    Google Scholar 

  2. Best, E., Devillers, R., Kiehn, A., Pomello, L. (1991) Concurrent bisimulations in Petri nets. Acta Informatica 28: 231-264

    MathSciNet  Google Scholar 

  3. Busi, N., Gorrieri, R. (1995) A Petri net semantics for \(\pi\)-calculus. Proc. Concur’95 (Lecture Notes in Computer Science), vol. 962. Springer, Berlin, pp. 145-159

  4. Caires, L., Cardelli, L. (2003) A spatial logic for concurrency (part I). Inform. and Comput. 186: 194-235

    Google Scholar 

  5. Cardelli, L., Gordon, A.D. (2000) Mobile ambients. Theoret. Comput. Sci. 240: 177-213

  6. Cardelli, L., Gordon, A.D. (2000) Anytime, anywhere. Modal logics for mobile ambients. Proc. POPL’00. ACM Press, New York, pp. 365-377

  7. Dal Zilio, S. (2000) Spatial congruence for ambients is decidable. Proc. ASIAN’00 - 6th Asian Computing Science Conference, Lecture Notes in Computer Science, Vol. 1961. Springer, Berlin, pp. 88-103

  8. Engelfriet, J. (1991) Branching processes of Petri nets. Acta Informatica 28: 575-591

    MathSciNet  Google Scholar 

  9. Engelfriet, J. (1996) A multiset semantics for the pi-calculus with replication. Theoret. Comput. Sci. 153: 65-94

    Google Scholar 

  10. Engelfriet, J., Gelsema, T.E. (1998) Axioms for generalized graphs, illustrated by a Cantor-Bernstein proposition. Acta Informatica 35: 1075-1096

    Article  MathSciNet  Google Scholar 

  11. Engelfriet, J., Gelsema, T.E. (1999) Multisets and structural congruence of the pi-calculus with replication. Theoret. Comput. Sci. 211: 311-337

    Google Scholar 

  12. Engelfriet, J., Gelsema, T.E. (2001) Structural inclusion in the pi-calculus with replication. Theoret. Comput. Sci. 258: 131-168

    Google Scholar 

  13. Goltz, U., Reisig, W. (1983) The non-sequential behaviour of Petri nets. Inf. and Control 57: 125-147

    MathSciNet  Google Scholar 

  14. Gordon, A.D. (2001) Notes on nominal calculi for security and mobility. Proc. FOSAD 2000, Lecture Notes in Computer Science, Vol. 2171. Springer, Berlin, pp. 262-330

  15. Hirschkoff, D. (1999) Mise en oeuvre de preuves de bisimulation. Ph.D. thesis, École Nationale des Ponts et Chaussées

  16. Hirschkoff, D., Lozes, E., Sangiorgi, D. (2002) Separability, expressiveness, and decidability in the ambient logic. Proc. LICS’02 IEEE Computer Society, pp. 423-432

  17. Honda, K., Tokoro, M. (1992) An object calculus for asynchronous communication. Proc. European Conference on Object-Oriented Programming, Lecture Notes in Computer Science, Vol. 512. Springer, Berlin, pp. 133-147

  18. Milner, R. (1997) Flowgraphs and flow algebras. J. of the ACM 26: 794-818

    Article  Google Scholar 

  19. Milner, R. (1989) Communication and concurrency. Prentice-Hall, Englewood Cliffs, NJ

  20. Milner, R. (1999) Communicating and mobile systems: the \(\pi\)-calculus. Cambridge University Press, Cambridge

    Google Scholar 

  21. Milner, R. (1993) The polyadic \(\pi\)-calculus: a tutorial. Logic and algebra of specification. Springer, Berlin, pp. 203-246

  22. Milner, R. (1992) Functions as processes. Math. Struct. in Comput. Sci. 2: 119-141

    Google Scholar 

  23. Milner, R., Parrow, J., Walker, D. (1992) A calculus of mobile processes. Inform. and Comput. 100: 1-77

    Google Scholar 

  24. Montanari, U., Pistore, M. (1995) Concurrent semantics for the \(\pi\)-calculus. Proc. MFCS’95 (Electronic Notes in Theoretical Computer Science, Vol. 1) Elsevier

  25. Olderog, E.-R. (1991) Nets, terms and formulas. Cambridge University Press, Cambridge

  26. Sangiorgi, D., Walker, D. (2001) The \(\pi\)-calculus: a theory of mobile processes. Cambridge University Press, Cambridge

  27. Schnoebelen, Ph., Sidorova, N. (2000) Bisimulation and the reduction of Petri nets. Proc. ICATPN’2000, Lecture Notes in Computer Science, Vol. 1825. Springer, Berlin, pp. 409-423

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Authors and Affiliations

  1. Leiden Institute of Advanced Computer Science, Leiden University, P.O.Box 9512, 2300 RA, Leiden, Netherlands

    Joost Engelfriet & Tjalling Gelsema

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  1. Joost Engelfriet
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  2. Tjalling Gelsema
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Correspondence to Joost Engelfriet.

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Received: 1 February 2000, Published online: 25 March 2004

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Engelfriet, J., Gelsema, T. A new natural structural congruence in the pi-calculus with replication. Acta Informatica 40, 385–430 (2004). https://doi.org/10.1007/s00236-004-0141-3

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  • DOI: https://doi.org/10.1007/s00236-004-0141-3

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